# Relative Conditional Probability

The ultimate goal of a rehabilitation or restoration plan is to achieve an ecosystem capable of self-propagation over time with no, or minimal, intervention. A fully functional ecosystem should be diverse and capable of resisting temporal and long-term changes in conditions like the loss or addition of species, or climate change.

The Figure below, illustrates some of the barriers to successful life-cycle development for biological organisms in mine rehabilitation. The first critical steps in rehabilitation of a native forest ecosystem is recruitment of individuals, through germination of the desired plant species, for these to resist adverse environmental conditions and find micro-sites for their initial survival, and achieve independence from the seed reserves (Barrier 1).

Figure 1 - Click image to enlarge

The next step of seedling development is dependent on the availability of nutrients to sustain growth, and the ability to compete with other plants (often weeds) for resources. Establishment of native plant species will be conditional on their ability to develop interactions with other organisms like nitrogen fixing bacteria or fungi, or phosphorus accumulating fungi (Barrier 2).

Another barrier that must be overcome is reproductive independence. Some of the factors required are: nutritional health for the production of reproductive structures, presence of pollinators and seed dispersal vectors. Animals will be able to migrate into a rehabilitation site if connected to remnant vegetation by corridors and assist with dispersal of new species into the area. The interconnectivity and the heterogeneous nature of a rehabilitation site, when established, will boost the development of biodiversity (Barrier 3) and add redundancy, a critical characteristic of “stable” ecosystems.

We are using these consecutive lifecycle barriers to develop a rehabilitation assessment technique, by calculating the probability of organisms successfully passing each barrier. This probability could be considered to be the number of survivors of the barrier compared to the number making the challenge. In addition, each of the probabilities under measure is conditional on the probability of a previous success. Thus, the probability of event B occurring is conditional on the probability that event A had occurred. For instance, the ability to grow is conditional on survival and, in turn, on the ability of seeds to germinate and emerge. Thus, the ability of different species to move through a string of events is the product of the probability of success in each of the individual events:

The string of events will eventually be closed as the life cycle is complete. This is a potentially useful concept but to what is this success to be measured? Thus, there needs to be a reference state against which to test success.

When assessing a rehabilitation site, whilst reconstructing a forest, the best material that might be hoped for is directly transferred forest soil from the target ecosystem in pristine condition. Thus, it could be argued that success on substitute material should be referenced to this type of soil in some way. This leads to the concept of relative conditional probability. Here we relate the probability of success for each event in each soil substitute to the probability of success in forest or woodland soil.

The relative conditional probability (RCP) of each growth medium tested is given by the following equation:

for n events in each medium under test.

This model has been trialled in the Spoil Amelioration Experiment and Topsoil Substitutes Experiments  projects. It will have other factors built into it, such as the restoration potential index, soil capacity for sustainable nutrition, and measures of bottlenecks and other barriers to natural ecosystem function.